The present invention relates to a species of diffractive optical element called chirp gratings as used in diffraction range finders.
Range finding by diffraction is comprised of the methods, devices and systems used to measure distance through exploitation of a phenomenon observed with diffraction gratings wherein the displacement between diffraction images of the various diffraction orders can be correlated to the distance from the grating to an observed source of energy illuminating the grating.
As postulated by Huygens over 3 centuries ago and proven experimentally by Thomas Young in 1801, if energy in the form of a periodic wave strikes an aperture, a new wave front is originated at said aperture. Diffraction gratings are surfaces with many adjacent apertures, typically in the form of ruled straight lines. When a wave front strikes a diffraction grating, new wave fronts originate from all apertures in the grating, and these new wave fronts then interfere with each other both constructively and destructively. Along lines of constructive interference, images can be formed in a receiver which is observing the grating. The images are called the diffraction orders.
The zero-order diffraction image appears along a direct line from the receiver to a source of energy (hereinafter called a xe2x80x9ctargetxe2x80x9d). Higher-order diffraction images of a target are reconstructed at the receiver, and they appear displaced to the side of the zero-order. As a target is moved toward or away from a grating surface, the relative displacement of a higher-order image from both the zero-order image and other higher-orders images can be used to measure target range.
The behavior of the higher-order diffraction images as a function of target distance has been previously reported in terms of plane gratings, that is, gratings with a fixed spacing between rules. Diffraction range finders that use plane gratings exhibit a characteristic relationship in the displacement of higher-order diffraction images. There is a maximum asymptotic limit to the displacement of the higher-order images which occurs when a target is at a very great distance from the grating. As a target approaches the grating, the displacement between higher-order images collapses. At point-of-contact with the grating, the higher-order images merge with each other and with the central zero-order image. The displacement of the higher-order images as a function of target distance is a parabolic dependency over the excursion of a target from infinite distance to point-of-contact with the grating. Therefore, the accuracy of a range finder made with plane diffraction gratings varies inversely with the square of the distance.
The behavior of diffraction range finders based on plane gratings is shown by example in the schematic diagram, FIG. 1(a), with correlated graph, FIG. 1(b).
FIG. 1(a) illustrates a diffraction range finder for use in the optical regime of light, that is, visible electromagnetic radiation. The device consists of a plane grating 110, a receiver in the form of a camera 200, and a structured illumination source in the form of a laser 300. The bundle of rays traced from the grating to the camera 150 show instances of the field-of-view of the lens 210 received in the camera. On the other side of the grating, the rays 160 are redirected by the action of the grating. Where these rays cross the line 320 representing the structured illumination, there will be a corresponding ray in the bundle 150. These points of intersection 330, marked with rectangles, are examples of range points that can be acquired by the range finder. They are mapped in the associated graph, FIG. 1(b), generated with equations (3) and (4). The graph trace 410 shows that along focal plane 220 there can be found a point x of the first-order image which correspond to target range D along the line of structured illumination 320. The illustrated case is a diffraction range finder using 635 nm illumination with a 1 micron pitch plane grating of 60 mm length as acquired with a camera with a 50 mm focal length lens.
Hyperbolic and parabolic relationships between target distance and image displacements are characteristic of conventional triangulation range finders as well as diffraction range finders made with plane gratings. The phenomenon is easily observed. For example, the stereo separation of human eyes resolves distance more accurately in the region at arm""s length than at distances near the limit of the eyes""ability to perceive two dimensional detail. Similarly, in triangulation range finders which use an active method of illumination such as a laser beam, resolution is inversely proportional to the square of the distance. This is a dependency similar to that found with diffraction range finders made with plane gratings.
An explanation for the inverse square relationship of accuracy to distance to be found in the triangulation and stereopsis range finding methods is that these range finders form the image of a target using a lens, and lenses generate images with perspective foreshortening. The mechanism by which a lens works dictates that as objects recede in distance from a lens, the images of objects of the same size will decrease in size on the focal plane of the lens. This is an observation which has informed perspective rendering since the Renaissance.
Perspective foreshortening can be seen in lenses of any focal length. FIGS. 2(a) and (b) show a schematic representation a camera 200 of focal plane dimension 220 with two lenses. The perspective foreshortening for the shorter focal length 230 shown in FIG. 2(a) is greater than that for the longer focal length 240 shown in FIG. 2(b), but both lenses show appreciable angles-of-view xcex8, 235 and 245.
FIG. 2(c) shows a characteristic graph trace 420 for the change in 255, view angle xcex8, as a function of 250, focal length F, in this instance for a 6.5 mm focal plane, typical for a half inch focal plane array. The angle can be known by                     θ        =                  2          ⁢                      xe2x80x83                    ⁢                      tan            ⁡                          (                              X                                  2                  ⁢                  F                                            )                                                          (        1        )            
where X is the length of the camera focal plane
The graph, FIG. 2(c), shows that as the focal length F increases, the angle of the field-of-view xcex8 narrows, but the asymptotically limited angle xcex8 does not reach zero degrees. The far-field accuracy of lens-based range finders can be increased by increasing the focal length of the lens used in the receiver. This will reduce foreshortening but not eliminate it. Moreover, long focal length lenses, such as telescopes, carry a significant weight and cost penalty in design utility. Depth-of-focus is also sacrificed with increased focal length. Additionally, in the case of range finders that use structured illumination such as a stripe or sheet of light for profilometry, the use of a long focal length will diminish the length of the stripe visible at the receiver and hence reduce the acquired profile length.
Diffraction range finders also may incorporate a lens to form an image of the higher-order diffraction images, but perspective effects of the lens are modified by the diffraction grating. Nonetheless, for diffraction range finders with plane gratings of fixed pitch, as have been used in all reported embodiments of diffraction range finders, a perspective-like effect is observed due to the use of a receiver with a lens to form the diffraction image. Again, the accuracy of the range instrument is inversely proportional to the square of the target distance. Indeed, the relationship between higher-order image deflection displacement and target distance follows the same parabolic shape as is characteristic of ranging systems based on the use of lenses such as triangulation and stereoscopy.
A prior art search was conducted. Patents that presage the present invention, wherein a range finder can be made with diffraction gratings are
U.S. Pat. No. 4,678,324 awarded to Tom DeWitt (now known as Tom Ditto, the co-inventor of the present invention) on Jul. 7, 1987 for xe2x80x9cRange Finding by Diffractionxe2x80x9d
U.S. Pat. No. 5,076,698 granted to Smith el al. on Dec. 31, 1991 for xe2x80x9cSensing the Shape of an Object.xe2x80x9d
The ""324 Patent supra defines a gratings as xe2x80x9coptical materials with equally spaced lines,xe2x80x9d [column 2, lines 61-62] and does not attempt to accommodate variable pitch gratings save for the case of compound gratings described therein as xe2x80x9cArrays of gratings . . . xe2x80x9d that is, xe2x80x9cmany pitches of diffraction gratings on a single substrata.xe2x80x9d [column 4, lines 4-11] The ""698 Patent supra, which cites ""324 Patent supra, assumes a plane grating and gives an example of a plane grating which is tuned to the argon wavelength.
The concept and fabrication of a variable pitch or chirp grating, upon which the present invention depends, is well known in the art. A common method of fabrication is holography. Holography was used by the present inventors for their realization of a working prototype of the present invention. Illustrative patents include:
U.S. Pat. No. 3,578,845 issued to Brooks el al. on May 18, 1971 for xe2x80x9cHolographic Focusing Diffraction Gratings for Spectroscopes and Method of Making Same.xe2x80x9d
U.S. Pat. No. 4,262,996 bestowed upon Yao on Apr. 21, 1981 for xe2x80x9cChirp-Grating Lens for Guided Wave Optics.xe2x80x9d
U.S. Pat. No. 5,238,531 earned by Macomber et al. on Aug. 24, 1993 for xe2x80x9cApparatus and Method for Fabricating a Chirped Grating in a Surface Emitting Distributed Feedback Semiconductor Laser Diode Device.xe2x80x9d
The ""845 Patent supra illustrates a holographic process for the fabrication of chirp gratings. In this instance, the resultant chirp grating is intended for spectroscopy. Other patented applications for chirp gratings include light wave guides and internal optics for lasers.
Because of the effects of perspective foreshortening found in triangulation range finders, optical systems have been invented that compensate for this limitation. An example of such systems can be found in
U.S. Pat. No. 4,875,777 issued to Harding on Oct. 24, 1989 for xe2x80x9cOff-Axis High Accuracy Structured Light Profiler.xe2x80x9d
The ""777 Patent supra is a triangulation range finding system that uses a combination of lenses and mirrors to improve performance, and when practiced by those knowledgeable in the art could overcome perspective foreshortening.
The applicants have found no patent that was issued for an invention that overcomes perspective foreshortening in the receiver of a diffraction range finder by means of a diffraction grating.
Pertinent non-patent publications of prior art written by the inventors are:
1) Thomas D. DeWitt and Douglas A. Lyon, xe2x80x9cA Range Finding Method Using Diffraction Gratings,xe2x80x9d Applied Optics, May 10, 1995, Vol. 34 No. 14, pp. 2510-2521
2) Thomas D. DeWitt and Douglas A. Lyon, xe2x80x9cThree-dimensional microscope using diffraction gratings,xe2x80x9d Three-Dimensional and Unconventional Imaging for Industrial Inspection and Metrology, SPIE, Vol. 2599, pp. 228-239
These publications, in particular the above referenced Applied Optics paper, are incorporated here by reference as if they were included verbatim and give instruction on diffraction theory as applied to diffraction range finders so as to further acquaint a reader with those facets of theory which are not explicitly detailed in the present text.
Prior art patents and other prior art documents cited above disclose the general concept of a variable pitch or chirp grating. Prior art also discloses methods of range finding by triangulation using lens and mirror systems to compensate for perspective foreshortening. Prior art includes range finding by fixed pitch gratings. The closest and the best prior art is by one of the co-inventors, Thomas Ditto (then named Thomas DeWitt), ""324 Patent supra.
Unfortunately none of the prior art devices singly or even in combination meets all of the objectives established by the inventors for a diffraction range finder. The present invention is the first to disclose methods, devices and systems for range finding utilizing variable pitch (or chirped) gratings.
1) The main objective of this invention is to specify a diffraction grating for a diffraction range finder with a pitch geometry such that perspective foreshortening in the receiver can be overcome.
2) It is further an object of this invention to specify a grating for a diffraction range finder that will generate higher-order displacements which are linear with respect to changes in target distance.
3) Still another object of this invention to generate higher-order displacements in a diffraction range finder that vary linearly as function of target distance.
4) An additional objective of this invention is to achieve a weight and size savings over range finding systems of equivalent performance based on mirrors and lenses.
5) Another objective of this invention is that it be robust in operation and require little maintenance or care.
6) A further objective of this invention is that it be extensible in application from a small scale instrument for microscopic range finding to large instruments for longer distances of many meters.
Objects and advantages of the invention have been set forth in part above and will be obvious in part from, or learned by practice with, the invention. The invention consists in the parts, constructions, embodiments and combinations, herein shown and described, or as may be inferred by reading this document.